PhD Chapter 1
Global - Analyses and regressions
This series of files compile analyses done for the global analysis of Chapter 1 (version of May 15th).
All analyses have been done with PRIMER-e 6 and R 3.6.3.
Click on the table of contents in the left margin to assess a specific analysis.
Click on a figure to zoom it
We used data from subtidal ecosystems (see metadata files for more information). Only stations that have been sampled both for abiotic parameters and benthic species were included.
Selected variables for the analyses:
- Percentage of organic matter: om
- Percentage of gravel: gravel
- Percentage of sand: sand
- Percentage of silt: silt
- Percentage of clay: clay
- Concentration of arsenic: arsenic
- Concentration of cadmium: cadmium
- Concentration of chromium: chromium
- Concentration of copper: copper
- Concentration of iron: iron
- Concentration of manganese: manganese
- Concentration of mercury: mercury
- Concentration of lead: lead
- Concentration of zinc: zinc
- Specific richness: S
- Total density of individuals: N
- Shannon’s diversity: H
- Piélou’s evenness: J
1. Data manipulation
For the following analyses, independant variables are habitat parameters and heavy metal concentrations, dependant variables are diversity indices. Variables have been standardized by mean and standard-deviation.
1.1. Identification of outliers
To identify stations that are not consistent with the others, we used the multivariate Cook’s Distance (CD) on the uncorrelated variables. A significative threshold of 4 times the mean of CD has been established.
0.5 community
We identified stations 30, 127, 138, 144, 183, 228, 237 as general outliers for habitat and stations 1, 11, 22, 25, 35, 127, 132, 139, 231 for metals. They have been deleted for the following analyses.
1 mm community
We identified stations 72, 82, 107, 129, 144, 202, 249 as general outliers for habitat and stations 106, 108, 110, 120, 127, 130, 139, 154, 232 for metals. They have been deleted for the following analyses.
1.2. Correlations between parameters
Correlations have been calculated with Spearman’s rank coefficient.
0.5 mm community
According to these results, the following variables are highly correlated (\(|\rho|\) > 0.80) so they have been considered together in the regressions:
- chromium, iron and manganese (iron and manganese deleted)
We decided to exclude silt content, as it tends to drasticaly increase VIFs due to a marginal correlation with sand (\(R^{2}_{adj}\) = 0.21).
| depth | om | gravel | sand | silt | clay | |
|---|---|---|---|---|---|---|
| depth | 1 | 0.298 | -0.26 | 0.209 | 0.497 | -0.483 |
| om | 0.298 | 1 | -0.504 | -0.407 | 0.479 | 0.01 |
| gravel | -0.26 | -0.504 | 1 | 0.019 | -0.347 | 0.162 |
| sand | 0.209 | -0.407 | 0.019 | 1 | -0.007 | -0.749 |
| silt | 0.497 | 0.479 | -0.347 | -0.007 | 1 | -0.534 |
| clay | -0.483 | 0.01 | 0.162 | -0.749 | -0.534 | 1 |
| arsenic | cadmium | chromium | copper | iron | manganese | mercury | lead | zinc | |
|---|---|---|---|---|---|---|---|---|---|
| arsenic | 1 | 0.732 | 0.631 | 0.713 | 0.405 | 0.62 | 0.711 | 0.865 | 0.808 |
| cadmium | 0.732 | 1 | 0.784 | 0.691 | 0.514 | 0.669 | 0.66 | 0.854 | 0.838 |
| chromium | 0.631 | 0.784 | 1 | 0.738 | 0.8 | 0.891 | 0.467 | 0.75 | 0.792 |
| copper | 0.713 | 0.691 | 0.738 | 1 | 0.571 | 0.738 | 0.612 | 0.843 | 0.928 |
| iron | 0.405 | 0.514 | 0.8 | 0.571 | 1 | 0.83 | 0.187 | 0.458 | 0.571 |
| manganese | 0.62 | 0.669 | 0.891 | 0.738 | 0.83 | 1 | 0.463 | 0.681 | 0.738 |
| mercury | 0.711 | 0.66 | 0.467 | 0.612 | 0.187 | 0.463 | 1 | 0.787 | 0.683 |
| lead | 0.865 | 0.854 | 0.75 | 0.843 | 0.458 | 0.681 | 0.787 | 1 | 0.928 |
| zinc | 0.808 | 0.838 | 0.792 | 0.928 | 0.571 | 0.738 | 0.683 | 0.928 | 1 |
1 mm community
According to these results, the following variables are highly correlated (\(|\rho|\) > 0.80) so they have been considered together in the regressions:
- om, silt and clay (silt deleted)
- chromium, iron and manganese (iron and manganese deleted)
| depth | om | gravel | sand | silt | clay | |
|---|---|---|---|---|---|---|
| depth | 1 | 0.442 | -0.026 | -0.328 | 0.317 | -0.097 |
| om | 0.442 | 1 | -0.304 | -0.798 | 0.841 | -0.125 |
| gravel | -0.026 | -0.304 | 1 | 0.124 | -0.383 | -0.023 |
| sand | -0.328 | -0.798 | 0.124 | 1 | -0.927 | -0.12 |
| silt | 0.317 | 0.841 | -0.383 | -0.927 | 1 | 0.069 |
| clay | -0.097 | -0.125 | -0.023 | -0.12 | 0.069 | 1 |
| arsenic | cadmium | chromium | copper | iron | manganese | mercury | lead | zinc | |
|---|---|---|---|---|---|---|---|---|---|
| arsenic | 1 | 0.743 | 0.79 | 0.809 | 0.636 | 0.707 | 0.702 | 0.892 | 0.88 |
| cadmium | 0.743 | 1 | 0.772 | 0.639 | 0.541 | 0.662 | 0.669 | 0.833 | 0.812 |
| chromium | 0.79 | 0.772 | 1 | 0.858 | 0.823 | 0.902 | 0.667 | 0.837 | 0.892 |
| copper | 0.809 | 0.639 | 0.858 | 1 | 0.77 | 0.792 | 0.708 | 0.857 | 0.946 |
| iron | 0.636 | 0.541 | 0.823 | 0.77 | 1 | 0.869 | 0.412 | 0.595 | 0.753 |
| manganese | 0.707 | 0.662 | 0.902 | 0.792 | 0.869 | 1 | 0.573 | 0.705 | 0.79 |
| mercury | 0.702 | 0.669 | 0.667 | 0.708 | 0.412 | 0.573 | 1 | 0.844 | 0.743 |
| lead | 0.892 | 0.833 | 0.837 | 0.857 | 0.595 | 0.705 | 0.844 | 1 | 0.928 |
| zinc | 0.88 | 0.812 | 0.892 | 0.946 | 0.753 | 0.79 | 0.743 | 0.928 | 1 |
2. Permutational Analyses of Variance
Results of univariate PermANOVAs on parameters and multivariate PermANOVA on the whole benthic community are presented in the table below. Variables have been standardized by mean and standard-deviation, and abundances were (log+1) transformed.
To be added.
3. Similarity and characteristic species
To be added.
4. Univariate regressions
We used linear models for the all regressions on diversity indices. Outliers and correlated variables were removed from these analyses. Variables have been standardized by mean and standard-deviation (coefficients need to be back-transformed to be used in predictive models).
4.1. Best model selection
This step was not used here as each models are necessary.
4.2. Significative variables selection
We identified which variables were selected after an AIC procedure to predict the best the parameters. Results of the variable selection, according to AIC, are shown on the tables below:
- for the 0.5 mm community:
| Variable (or combination) | S | N | H | J |
|---|---|---|---|---|
| depth | + | - | + | + |
| om/silt | + | + | - | |
| gravel | + | + | + | |
| sand | + | + | - | |
| clay | + | + | + | - |
| Adjusted \(R^{2}\) | 0.33 | 0.5 | 0.27 | 0.16 |
| Variable (or combination) | S | N | H | J |
|---|---|---|---|---|
| arsenic | - | - | ||
| cadmium | - | - | ||
| chromium/iron/manganese | + | - | - | |
| mercury | - | - | ||
| lead/copper/zinc | + | + | ||
| Adjusted \(R^{2}\) | 0.18 | 0.49 | 0.07 | 0.02 |
- for the 1 mm community:
| Variable (or combination) | S | N | H | J |
|---|---|---|---|---|
| depth | + | - | + | + |
| om/silt | ||||
| gravel | - | |||
| sand | - | - | - | |
| clay | - | - | - | |
| Adjusted \(R^{2}\) | 0.25 | 0.03 | 0.34 | 0.1 |
| Variable (or combination) | S | N | H | J |
|---|---|---|---|---|
| arsenic | ||||
| cadmium | - | - | ||
| chromium/iron/manganese | ||||
| mercury | ||||
| lead/copper/zinc | + | + | ||
| Adjusted \(R^{2}\) | 0.08 | 0 | 0.05 | 0 |
Details of the regressions, with diagnostics and cross-validation, are summarized below.
0.5 mm community
Richness/habitat
## FULL MODEL
## Adjusted R2 is: 0.33
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | 0.02378 | 0.06373 | 0.3732 | 0.7095 | |
| depth | 0.2425 | 0.07287 | 3.328 | 0.001097 | * * |
| om | 0.2862 | 0.07987 | 3.584 | 0.0004548 | * * * |
| gravel | 0.2016 | 0.09011 | 2.237 | 0.0267 | * |
| sand | 0.2542 | 0.1164 | 2.183 | 0.03054 | * |
| clay | 0.7458 | 0.1126 | 6.623 | 5.636e-10 | * * * |
## RMSE from cross-validation: 0.8090011
| depth | om | gravel | sand | clay | |
|---|---|---|---|---|---|
| VIF | 1.14 | 1.25 | 1.05 | 1.84 | 1.79 |
## REDUCED MODEL
## Adjusted R2 is: 0.33
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | 0.02378 | 0.06373 | 0.3732 | 0.7095 | |
| depth | 0.2425 | 0.07287 | 3.328 | 0.001097 | * * |
| om | 0.2862 | 0.07987 | 3.584 | 0.0004548 | * * * |
| gravel | 0.2016 | 0.09011 | 2.237 | 0.0267 | * |
| sand | 0.2542 | 0.1164 | 2.183 | 0.03054 | * |
| clay | 0.7458 | 0.1126 | 6.623 | 5.636e-10 | * * * |
## RMSE from cross-validation: 0.8090011
| depth | om | gravel | sand | clay | |
|---|---|---|---|---|---|
| VIF | 1.14 | 1.25 | 1.05 | 1.84 | 1.79 |
Density/habitat
## FULL MODEL
## Adjusted R2 is: 0.5
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | 0.01472 | 0.05775 | 0.2548 | 0.7992 | |
| depth | -0.09499 | 0.06604 | -1.438 | 0.1524 | |
| om | 0.5369 | 0.07238 | 7.418 | 7.649e-12 | * * * |
| gravel | 0.1221 | 0.08167 | 1.495 | 0.137 | |
| sand | 0.5185 | 0.1055 | 4.914 | 2.27e-06 | * * * |
| clay | 0.8915 | 0.1021 | 8.736 | 3.96e-15 | * * * |
## RMSE from cross-validation: 0.7850903
| depth | om | gravel | sand | clay | |
|---|---|---|---|---|---|
| VIF | 1.14 | 1.25 | 1.05 | 1.84 | 1.79 |
## REDUCED MODEL
## Adjusted R2 is: 0.5
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | 0.01472 | 0.05775 | 0.2548 | 0.7992 | |
| depth | -0.09499 | 0.06604 | -1.438 | 0.1524 | |
| om | 0.5369 | 0.07238 | 7.418 | 7.649e-12 | * * * |
| gravel | 0.1221 | 0.08167 | 1.495 | 0.137 | |
| sand | 0.5185 | 0.1055 | 4.914 | 2.27e-06 | * * * |
| clay | 0.8915 | 0.1021 | 8.736 | 3.96e-15 | * * * |
## RMSE from cross-validation: 0.7850903
| depth | om | gravel | sand | clay | |
|---|---|---|---|---|---|
| VIF | 1.14 | 1.25 | 1.05 | 1.84 | 1.79 |
Diversity/habitat
## FULL MODEL
## Adjusted R2 is: 0.26
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | 0.05663 | 0.06356 | 0.891 | 0.3743 | |
| depth | 0.5219 | 0.07268 | 7.181 | 2.822e-11 | * * * |
| om | 0.01009 | 0.07966 | 0.1267 | 0.8993 | |
| gravel | 0.156 | 0.08988 | 1.735 | 0.08467 | |
| sand | -0.07361 | 0.1161 | -0.6339 | 0.5271 | |
| clay | 0.2279 | 0.1123 | 2.029 | 0.04422 | * |
## RMSE from cross-validation: 0.8101494
| depth | om | gravel | sand | clay | |
|---|---|---|---|---|---|
| VIF | 1.14 | 1.25 | 1.05 | 1.84 | 1.79 |
## REDUCED MODEL
## Adjusted R2 is: 0.27
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | 0.05587 | 0.06327 | 0.883 | 0.3786 | |
| depth | 0.535 | 0.07073 | 7.565 | 3.221e-12 | * * * |
| gravel | 0.1584 | 0.08587 | 1.844 | 0.06707 | |
| clay | 0.2884 | 0.06988 | 4.127 | 5.989e-05 | * * * |
## RMSE from cross-validation: 0.8019987
| depth | gravel | clay | |
|---|---|---|---|
| VIF | 1.11 | 1 | 1.12 |
Evenness/habitat
## FULL MODEL
## Adjusted R2 is: 0.15
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | 0.05235 | 0.06563 | 0.7977 | 0.4263 | |
| depth | 0.3094 | 0.07505 | 4.122 | 6.142e-05 | * * * |
| om | -0.1443 | 0.08226 | -1.754 | 0.08146 | |
| gravel | -0.004248 | 0.09281 | -0.04577 | 0.9636 | |
| sand | -0.2053 | 0.1199 | -1.712 | 0.08889 | |
| clay | -0.2228 | 0.116 | -1.921 | 0.05654 |
## RMSE from cross-validation: 0.8333639
| depth | om | gravel | sand | clay | |
|---|---|---|---|---|---|
| VIF | 1.14 | 1.25 | 1.05 | 1.84 | 1.79 |
## REDUCED MODEL
## Adjusted R2 is: 0.16
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | 0.05272 | 0.06493 | 0.8119 | 0.4181 | |
| depth | 0.3095 | 0.07478 | 4.138 | 5.741e-05 | * * * |
| om | -0.1432 | 0.07888 | -1.816 | 0.07132 | |
| sand | -0.2041 | 0.1168 | -1.748 | 0.08245 | |
| clay | -0.2218 | 0.1134 | -1.956 | 0.05228 |
## RMSE from cross-validation: 0.8267531
| depth | om | sand | clay | |
|---|---|---|---|---|
| VIF | 1.14 | 1.21 | 1.8 | 1.75 |
Richness/metals
## FULL MODEL
## Adjusted R2 is: 0.17
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | -0.06047 | 0.0758 | -0.7978 | 0.4264 | |
| arsenic | -0.4048 | 0.1342 | -3.017 | 0.003051 | * * |
| cadmium | -0.6834 | 0.1672 | -4.087 | 7.426e-05 | * * * |
| chromium | -0.01251 | 0.138 | -0.09062 | 0.9279 | |
| mercury | -0.4632 | 0.1701 | -2.723 | 0.007325 | * * |
| lead | 1.038 | 0.2052 | 5.06 | 1.333e-06 | * * * |
## RMSE from cross-validation: 0.8958299
| arsenic | cadmium | chromium | mercury | lead | |
|---|---|---|---|---|---|
| VIF | 1.56 | 2.08 | 1.75 | 1.43 | 2.7 |
## REDUCED MODEL
## Adjusted R2 is: 0.18
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | -0.05982 | 0.07518 | -0.7956 | 0.4276 | |
| arsenic | -0.4045 | 0.1337 | -3.026 | 0.002957 | * * |
| cadmium | -0.6892 | 0.154 | -4.474 | 1.6e-05 | * * * |
| mercury | -0.4584 | 0.161 | -2.847 | 0.005086 | * * |
| lead | 1.031 | 0.19 | 5.427 | 2.524e-07 | * * * |
## RMSE from cross-validation: 0.8902463
| arsenic | cadmium | mercury | lead | |
|---|---|---|---|---|
| VIF | 1.56 | 1.92 | 1.36 | 2.51 |
Density/metals
## FULL MODEL
## Adjusted R2 is: 0.49
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | -0.1098 | 0.05881 | -1.867 | 0.06407 | |
| arsenic | -0.5128 | 0.1041 | -4.926 | 2.398e-06 | * * * |
| cadmium | -0.7432 | 0.1297 | -5.729 | 6.212e-08 | * * * |
| chromium | 0.2695 | 0.1071 | 2.517 | 0.01301 | * |
| mercury | -0.7299 | 0.132 | -5.529 | 1.588e-07 | * * * |
| lead | 1.43 | 0.1592 | 8.986 | 1.907e-15 | * * * |
## RMSE from cross-validation: 0.7065136
| arsenic | cadmium | chromium | mercury | lead | |
|---|---|---|---|---|---|
| VIF | 1.56 | 2.08 | 1.75 | 1.43 | 2.7 |
## REDUCED MODEL
## Adjusted R2 is: 0.49
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | -0.1098 | 0.05881 | -1.867 | 0.06407 | |
| arsenic | -0.5128 | 0.1041 | -4.926 | 2.398e-06 | * * * |
| cadmium | -0.7432 | 0.1297 | -5.729 | 6.212e-08 | * * * |
| chromium | 0.2695 | 0.1071 | 2.517 | 0.01301 | * |
| mercury | -0.7299 | 0.132 | -5.529 | 1.588e-07 | * * * |
| lead | 1.43 | 0.1592 | 8.986 | 1.907e-15 | * * * |
## RMSE from cross-validation: 0.7065136
| arsenic | cadmium | chromium | mercury | lead | |
|---|---|---|---|---|---|
| VIF | 1.56 | 2.08 | 1.75 | 1.43 | 2.7 |
Diversity/metals
## FULL MODEL
## Adjusted R2 is: 0.06
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | 0.03115 | 0.07881 | 0.3952 | 0.6933 | |
| arsenic | -0.115 | 0.1395 | -0.8244 | 0.4112 | |
| cadmium | -0.2287 | 0.1738 | -1.316 | 0.1905 | |
| chromium | -0.2563 | 0.1435 | -1.786 | 0.0764 | |
| mercury | 0.02354 | 0.1769 | 0.1331 | 0.8943 | |
| lead | 0.2542 | 0.2133 | 1.192 | 0.2355 |
## RMSE from cross-validation: 0.9303706
| arsenic | cadmium | chromium | mercury | lead | |
|---|---|---|---|---|---|
| VIF | 1.56 | 2.08 | 1.75 | 1.43 | 2.7 |
## REDUCED MODEL
## Adjusted R2 is: 0.07
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | 0.0391 | 0.077 | 0.5078 | 0.6124 | |
| chromium | -0.2812 | 0.08139 | -3.455 | 0.0007288 | * * * |
## RMSE from cross-validation: 0.9157629
| chromium | |
|---|---|
| VIF | 1 |
Evenness/metals
## FULL MODEL
## Adjusted R2 is: 0.03
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | 0.07716 | 0.07843 | 0.9838 | 0.3269 | |
| arsenic | 0.1621 | 0.1388 | 1.167 | 0.2451 | |
| cadmium | 0.2536 | 0.173 | 1.466 | 0.145 | |
| chromium | -0.238 | 0.1428 | -1.666 | 0.09799 | |
| mercury | 0.1657 | 0.176 | 0.9411 | 0.3483 | |
| lead | -0.3184 | 0.2123 | -1.5 | 0.1359 |
## RMSE from cross-validation: 0.9265784
| arsenic | cadmium | chromium | mercury | lead | |
|---|---|---|---|---|---|
| VIF | 1.56 | 2.08 | 1.75 | 1.43 | 2.7 |
## REDUCED MODEL
## Adjusted R2 is: 0.02
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | 0.05581 | 0.07726 | 0.7224 | 0.4713 | |
| chromium | -0.1744 | 0.08166 | -2.136 | 0.03445 | * |
## RMSE from cross-validation: 0.9269077
| chromium | |
|---|---|
| VIF | 1 |
1 mm community
Richness/habitat
## FULL MODEL
## Adjusted R2 is: 0.25
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | -0.04634 | 0.06256 | -0.7407 | 0.4598 | |
| depth | 0.2715 | 0.06482 | 4.188 | 4.307e-05 | * * * |
| om | -0.04458 | 0.1117 | -0.3991 | 0.6903 | |
| gravel | -0.1185 | 0.08561 | -1.384 | 0.1679 | |
| sand | -0.4367 | 0.1322 | -3.304 | 0.001141 | * * |
| clay | -0.5032 | 0.1403 | -3.586 | 0.0004272 | * * * |
## RMSE from cross-validation: 0.8934522
| depth | om | gravel | sand | clay | |
|---|---|---|---|---|---|
| VIF | 1.06 | 1.81 | 1.03 | 2.1 | 1.45 |
## REDUCED MODEL
## Adjusted R2 is: 0.25
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | -0.03361 | 0.06184 | -0.5436 | 0.5874 | |
| depth | 0.2678 | 0.06475 | 4.136 | 5.298e-05 | * * * |
| sand | -0.3869 | 0.07612 | -5.083 | 8.825e-07 | * * * |
| clay | -0.4563 | 0.114 | -4.001 | 9.001e-05 | * * * |
## RMSE from cross-validation: 0.8673699
| depth | sand | clay | |
|---|---|---|---|
| VIF | 1.06 | 1.21 | 1.18 |
Density/habitat
## FULL MODEL
## Adjusted R2 is: 0.02
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | -0.0211 | 0.07296 | -0.2892 | 0.7727 | |
| depth | -0.1713 | 0.07559 | -2.266 | 0.02458 | * |
| om | -0.09757 | 0.1303 | -0.749 | 0.4548 | |
| gravel | 0.002914 | 0.09984 | 0.02919 | 0.9767 | |
| sand | -0.29 | 0.1542 | -1.881 | 0.06147 | |
| clay | -0.3748 | 0.1636 | -2.291 | 0.02309 | * |
## RMSE from cross-validation: 1.008745
| depth | om | gravel | sand | clay | |
|---|---|---|---|---|---|
| VIF | 1.06 | 1.81 | 1.03 | 2.1 | 1.45 |
## REDUCED MODEL
## Adjusted R2 is: 0.03
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | -0.01888 | 0.07186 | -0.2627 | 0.7931 | |
| depth | -0.1719 | 0.07525 | -2.285 | 0.02341 | * |
| sand | -0.1969 | 0.08846 | -2.226 | 0.02718 | * |
| clay | -0.3066 | 0.1325 | -2.314 | 0.02174 | * |
## RMSE from cross-validation: 1.002598
| depth | sand | clay | |
|---|---|---|---|
| VIF | 1.06 | 1.21 | 1.18 |
Diversity/habitat
## FULL MODEL
## Adjusted R2 is: 0.34
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | -0.02566 | 0.05866 | -0.4374 | 0.6623 | |
| depth | 0.4303 | 0.06078 | 7.079 | 2.765e-11 | * * * |
| om | 0.06608 | 0.1047 | 0.631 | 0.5288 | |
| gravel | -0.1077 | 0.08027 | -1.341 | 0.1815 | |
| sand | -0.2444 | 0.124 | -1.971 | 0.05013 | |
| clay | -0.2757 | 0.1316 | -2.096 | 0.03742 | * |
## RMSE from cross-validation: 0.8438226
| depth | om | gravel | sand | clay | |
|---|---|---|---|---|---|
| VIF | 1.06 | 1.81 | 1.03 | 2.1 | 1.45 |
## REDUCED MODEL
## Adjusted R2 is: 0.34
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | -0.02847 | 0.0584 | -0.4875 | 0.6265 | |
| depth | 0.4311 | 0.06067 | 7.105 | 2.348e-11 | * * * |
| gravel | -0.119 | 0.0781 | -1.524 | 0.1292 | |
| sand | -0.3082 | 0.07143 | -4.315 | 2.564e-05 | * * * |
| clay | -0.3236 | 0.1073 | -3.017 | 0.002901 | * * |
## RMSE from cross-validation: 0.8399062
| depth | gravel | sand | clay | |
|---|---|---|---|---|
| VIF | 1.06 | 1.01 | 1.21 | 1.18 |
Evenness/habitat
## FULL MODEL
## Adjusted R2 is: 0.08
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | 0.01566 | 0.06839 | 0.2289 | 0.8192 | |
| depth | 0.2928 | 0.07086 | 4.133 | 5.383e-05 | * * * |
| om | 0.02954 | 0.1221 | 0.2419 | 0.8091 | |
| gravel | 0.008159 | 0.09359 | 0.08718 | 0.9306 | |
| sand | -0.04328 | 0.1445 | -0.2995 | 0.7649 | |
| clay | -0.02071 | 0.1534 | -0.135 | 0.8927 |
## RMSE from cross-validation: 0.9552492
| depth | om | gravel | sand | clay | |
|---|---|---|---|---|---|
| VIF | 1.06 | 1.81 | 1.03 | 2.1 | 1.45 |
## REDUCED MODEL
## Adjusted R2 is: 0.1
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | 0.01448 | 0.0664 | 0.2181 | 0.8276 | |
| depth | 0.3126 | 0.06602 | 4.735 | 4.225e-06 | * * * |
## RMSE from cross-validation: 0.9358617
| depth | |
|---|---|
| VIF | 1 |
Richness/metals
## FULL MODEL
## Adjusted R2 is: 0.07
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | 0.06323 | 0.08253 | 0.7661 | 0.4451 | |
| arsenic | -0.1466 | 0.1335 | -1.098 | 0.2742 | |
| cadmium | -0.5481 | 0.1606 | -3.413 | 0.0008755 | * * * |
| chromium | 0.01217 | 0.1638 | 0.07431 | 0.9409 | |
| mercury | -0.001392 | 0.1293 | -0.01077 | 0.9914 | |
| lead | 0.4503 | 0.2727 | 1.651 | 0.1013 |
## RMSE from cross-validation: 0.9298714
| arsenic | cadmium | chromium | mercury | lead | |
|---|---|---|---|---|---|
| VIF | 1.65 | 1.85 | 1.89 | 1.48 | 3.17 |
## REDUCED MODEL
## Adjusted R2 is: 0.08
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | 0.06172 | 0.08196 | 0.7531 | 0.4529 | |
| cadmium | -0.5082 | 0.149 | -3.409 | 0.000881 | * * * |
| lead | 0.3104 | 0.1476 | 2.103 | 0.03751 | * |
## RMSE from cross-validation: 0.9219954
| cadmium | lead | |
|---|---|---|
| VIF | 1.73 | 1.73 |
Density/metals
## FULL MODEL
## Adjusted R2 is: -0.01
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | 0.01452 | 0.09066 | 0.1602 | 0.873 | |
| arsenic | -0.1569 | 0.1467 | -1.07 | 0.287 | |
| cadmium | -0.161 | 0.1764 | -0.9126 | 0.3633 | |
| chromium | -0.2011 | 0.18 | -1.117 | 0.2661 | |
| mercury | -0.1079 | 0.142 | -0.7597 | 0.4489 | |
| lead | 0.4704 | 0.2995 | 1.57 | 0.1189 |
## RMSE from cross-validation: 1.030112
| arsenic | cadmium | chromium | mercury | lead | |
|---|---|---|---|---|---|
| VIF | 1.65 | 1.85 | 1.89 | 1.48 | 3.17 |
## REDUCED MODEL
## Adjusted R2 is: 0
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | 0.01849 | 0.08981 | 0.2058 | 0.8373 |
## RMSE from cross-validation: 1.011527
Quitting from lines 440-442 (C1_analyses_B.Rmd) Error in Qr$qr[p1, p1, drop = FALSE] : indice hors limites De plus : There were 33 warnings (use warnings() to see them)
Diversity/metals
## FULL MODEL
## Adjusted R2 is: 0.04
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | 0.09394 | 0.08016 | 1.172 | 0.2435 | |
| arsenic | -0.1326 | 0.1297 | -1.023 | 0.3086 | |
| cadmium | -0.4559 | 0.156 | -2.923 | 0.004141 | * * |
| chromium | 0.006562 | 0.1591 | 0.04124 | 0.9672 | |
| mercury | 0.03018 | 0.1255 | 0.2404 | 0.8104 | |
| lead | 0.3954 | 0.2648 | 1.493 | 0.1381 |
## RMSE from cross-validation: 0.8995954
| arsenic | cadmium | chromium | mercury | lead | |
|---|---|---|---|---|---|
| VIF | 1.65 | 1.85 | 1.89 | 1.48 | 3.17 |
## REDUCED MODEL
## Adjusted R2 is: 0.05
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | 0.09219 | 0.07962 | 1.158 | 0.2492 | |
| cadmium | -0.4268 | 0.1448 | -2.948 | 0.003831 | * * |
| lead | 0.2923 | 0.1434 | 2.038 | 0.04365 | * |
## RMSE from cross-validation: 0.8942355
| cadmium | lead | |
|---|---|---|
| VIF | 1.73 | 1.73 |
Evenness/metals
## FULL MODEL
## Adjusted R2 is: -0.04
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | 0.06202 | 0.07961 | 0.779 | 0.4375 | |
| arsenic | -0.05693 | 0.1288 | -0.4421 | 0.6592 | |
| cadmium | -0.04309 | 0.1549 | -0.2782 | 0.7813 | |
| chromium | 0.05701 | 0.158 | 0.3607 | 0.7189 | |
| mercury | 0.03799 | 0.1247 | 0.3047 | 0.7611 | |
| lead | -0.004916 | 0.263 | -0.01869 | 0.9851 |
## RMSE from cross-validation: 0.8928066
| arsenic | cadmium | chromium | mercury | lead | |
|---|---|---|---|---|---|
| VIF | 1.65 | 1.85 | 1.89 | 1.48 | 3.17 |
## REDUCED MODEL
## Adjusted R2 is: 0
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | 0.06244 | 0.07799 | 0.8006 | 0.4249 |
## RMSE from cross-validation: 0.873627
Quitting from lines 464-466 (C1_analyses_B.Rmd) Error in Qr\(qr[p1, p1, drop = FALSE] : indice hors limites De plus : Warning messages: 1: In CVlm(data = lm_out\)model, form.lm = lm_out, m = 5, printit = F) :
As there is >1 explanatory variable, cross-validation predicted values for a fold are not a linear function of corresponding overall predicted values. Lines that are shown for the different folds are approximate
2: In CVlm(data = lm_out$model, form.lm = lm_out, m = 5, printit = F) :
As there is >1 explanatory variable, cross-validation predicted values for a fold are not a linear function of corresponding overall predicted values. Lines that are shown for the different folds are approximate
3: In CVlm(data = lm_out$model, form.lm = lm_out, m = 5, printit = F) :
As there is >1 explanatory variable, cross-validation predicted values for a fold are not a linear function of corresponding overall predicted values. Lines that are shown for the different folds are approximate
4: In CVlm(data = lm_out$model, form.lm = lm_out, m = 5, printit = F) :
As there is >1 explanatory variable, cross-validation predicted values for a fold are not a linear function of corresponding overall predicted values. Lines that are shown for the different folds are approximate
5. Multivariate regression
To be added.